On properties of the special coordinate basis of linear systems

Abstract

In this paper, we provide, for the first time in the literature, rigorous and complete proofs to all the key properties of the special coordinate basis of linear timeinvariant systems. The special coordinate basis decomposition or technique developed by Sannuti and Saberi in 1987 has a distinct feature of explicitly displaying the finite and infinite zero structures, the invertibility structures, as well as the invariant and almost invariant geometric subspaces of a given system. The technique has been extensively used in the literature to solve many system and control problems. We believe that the result of this paper is a complement of the seminal work of Sannuti and Saberi. It makes the theory of the special coordinate basis more complete.